(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a sequence [tex]a_{n}[/tex] which is non-negative and null but where [tex]\sum (-1)^{n+1} a_{n}[/tex] is divergent.

2. Relevant equations

Alternating series test:

Let [tex]a_{n}[/tex] be a decreasing sequence of positive real numbers such that [tex]a_{n}\rightarrowa[/tex] as [tex]n\rightarrow\infty[/tex]. Then the series [tex]\sum (-1)^{n+1} a_{n}[/tex] converges.

3. The attempt at a solution

I'm a bit confused by this one. If [tex]a_{n}[/tex] is non-negative and null then it seems like it's decreasing to zero, in which case it satisfies the alternating series test. So how can the sum diverge?!

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# Homework Help: Alternating series test

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